Thanks! could you please explain further how you know this to be true?
If you look here: http://en.wikipedia.org/wiki/Trajectory#Range_and_height
I'm assuming x is the max range R?
Then y = vi2sin2(θ)/2g = vi2/2g * (1 - cos2(θ))
Now if this were to match the equation in OP, then we need
vi2cos2(θ)/2g = gR2/2vi2
But subbing in R = vi2sin(2θ)/g, we get
vi2cos2(θ)/2g = vi2sin2(2θ)/2g
But cos2(θ) =/= sin2(2θ)